US Secretary of State Antony Blinken said after talks with Russia's foreign minister on Friday that Moscow would face a "swift, severe and a united response" if it invades Ukraine.
Blinken said after the talks in Geneva that Washington had agreed to provide written comments to Russia after Moscow demanded security guarantees, including a pledge that Ukraine will never be able to join NATO.
He described Friday's talks with Russian Foreign Minister Sergei Lavrov, intended to reduce tensions that have risen since Russia massed troops near Ukraine's border, as frank and useful.
Read more: Russia, US cast pall on Ukraine talks
"We've been clear - if any Russian military forces move across Ukraine's border, that's a renewed invasion. It will be met with swift, severe and a united response from the United States and our partners and allies," Blinken told a news conference in Geneva.
Western states fear Moscow is planning a new assault on Ukraine after sending in forces into the former Soviet republic 2014 to annex the Crimea peninsula. Russia denies planning an attack but says it could take unspecified military action if its security demands are not met.
Also read: Germany says Russia will pay price if it moves on Ukraine
Blinken said Washington had sought during Friday's talks to determine whether Moscow was prepared to take a diplomatic path to defuse tensions over Ukraine.
Both sides agreed it was important for the diplomatic process to continue, he said.
Lavrov said after meeting Blinken that he hoped that emotions would cool down over Ukraine and repeated Russian assertions that it poses no threat to its neighbour.
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